We test the ability of large scale velocity fields inferred from geomagnetic secular variation data to produce the global magnetic field of the Earth.Our kinematic dynamo calculations use quasi-geostrophic (QG) flows inverted from geomagnetic field models which, as such, incorporate flow structures that are Earth-like and may be important for the geodynamo.Furthermore, the QG hypothesis allows straightforward prolongation of the flow from the core surface to the bulk.As expected from previous studies, we check that a simple quasi-geostrophic flow is not able to sustain the magnetic field against ohmic decay.Additional complexity is then introduced in the flow, inspired by the action of the Lorentz force.Indeed, on centenial time-scales, the Lorentz force can balance the Coriolis force and strict quasi-geostrophy may not be the best ansatz.When the columnar flow is modified to account for the action of the Lorentz force, magnetic field is generated for Elsasser numbers larger than 0.25 and magnetic Reynolds numbers larger than 100.This suggests that our large scale flow captures the relevant features for the generation of the Earth's magnetic field and that the invisible small scale flow may not be directly involved in this process.Near the threshold, the resulting magnetic field is dominated by an axial dipole, with some reversed flux patches.Time-dependence is also considered, derived from principal component analysis applied to the inverted flows.We find that time periods from 120 to 50 years do not affect the mean growth rate of the kinematic dynamos.Finally we notice the footprint of the inner-core in the magnetic field generated deep in the bulk of the shell, although we did not include one in our computations.
Current "Earth-like" numerical dynamo simulations are able to reproduce many characteristics of the observed geomagnetic field. One notable exception is the geomagnetic octupolar component. Here we investigate whether a stably stratified layer at the top of the core, a missing ingredient in standard dynamo simulations, can explain the observed geomagnetic octupole. Through numerical simulations, we find that the existence of a stable layer has significant influence on the octupolar-to-dipolar ratio of the magnetic field. Particularly, we find that a 60 km stable layer with relatively strong st…
It is proposed that convection driven dynamos operating in planetary cores could be oscillatory even when the oscillations are not directly noticeable from the outside. Examples of dynamo simulations are pointed out that exhibit oscillations in the structure of the azimuthally averaged toroidal magnetic flux while the mean poloidal field shows only variations in its amplitude. In the case of the geomagnetic field, global excursions may be associated with these oscillations. Long period dynamo simulations indicate that the oscillations may cause reversals once in a while. No special attempt has…
Variations in the geomagnetic field occur on a vast range of time scales, from milliseconds to millions of years. The advent of satellite measurements has allowed for detailed studies of the short timescale geomagnetic field behaviour, but understanding the long timescale evolution remains challenging due to the sparsity of the paleomagnetic record. This paper introduces a field theory framework for studying magnetic field generation as a result of stochastic fluid motions. By constructing a stochastic kinematic dynamo model, we derive statistical properties of the magnetic field that may be c…
The behaviour of the geomagnetic field characteristics (mean values of the paleointensity, amplitude of its variations and reversal frequency) during the last 170 million years was analyzed. It was found that the mean values of the paleointensity were in direct relation to amplitude of its variations and in reverse relation to reversal frequency. The most considerable changes of the Earth magnetic field characteristics occurred in Early Cretaceous, Middle Paleogene and Neogene. The analysis of conformity of the reconstructed characteristics behaviour of a geomagnetic field to an alfa-omega- dy…
Here we present datasets of daily variation obtained from the geomagnetic field raw observations recorded at the Coimbra Magnetic Observatory (COI, Portugal) in 2007-2017, covering almost the entire solar cycle 24. Two methods were used to extract daily variability from the raw geomagnetic hourly data. The first method uses the so-called geomagnetically quiet days to calculate S-type variations as daily means resulting in the data sub-set named IQD Sq and SD. The second method uses the principal component analysis (PCA) to decompose the original series into main variability modes. The first th…
The purpose of this communication is to suggest that the mechanism for generating the geomagnetic field and the energy source for powering it are one and the same, a nuclear georeactor at the center of the Earth. Toward this end, I: i) Present evidence that the nuclear georeactor fission-product sub-shell is fluid; ii)Suggest that the geomagnetic field is generated within the georeactor sub-shell, rather than within Earth's iron-alloy fluid core; iii) Describe why convection appears more feasible within the georeactor sub-shell than within the iron-alloy core; iv) Disclose additional relative …
Statistical properties of the temporal distribution of polarity reversals of the geomagnetic field are commonly assumed to be a realization of a renewal Poisson process with a variable rate. However, it has been recently shown that the polarity reversals strongly depart from a local Poisson statistics, because of temporal clustering. Such clustering arises from the presence of long-range correlations in the underlying dynamo process. Recently achieved laboratory dynamo also shows reversals. It is shown here that laboratory and paleomagnetic data are both characterized by the presence of long-r…
One of the most fundamental problems in physics has been to understand the nature of the mechanism that generates the geomagnetic field and the magnetic fields of other planets and satellites. For decades, the dynamo mechanism, thought to be responsible for generating the geomagnetic field and other planetary magnetic fields, has been ascribed to convection in each planet's iron-alloy core. Recently, I described the problems inherent in Earth-core convection and proposed instead that the geomagnetic field is produced by a dynamo mechanism involving convection, not in the fluid core, but in the…
Often in nature the temporal distribution of inhomogeneous stochastic point processes can be modeled as a realization of renewal Poisson processes with a variable rate. Here we investigate one of the classical examples, namely the temporal distribution of polarity reversals of the geomagnetic field. In spite of the commonly used underlying hypothesis, we show that this process strongly departs from a Poisson statistics, the origin of this failure stemming from the presence of temporal clustering. We find that a Levy statistics is able to reproduce paleomagnetic data, thus suggesting the presen…
Using a mean-field dynamo model with a spherically symmetric helical turbulence parameter alpha which is dynamically quenched and disturbed by additional noise, the basic features of geomagnetic polarity reversals are shown to be generic consequences of the dynamo action in the vicinity of exceptional points of the spectrum. This simple paradigmatic model yields long periods of constant polarity which are interrupted by self-accelerating field decays leading to asymmetric polarity reversals. It shows the recently discovered bimodal field distribution, and it gives a natural explanation of the …
Convection in the liquid outer core of the Earth is driven by thermal and chemical perturbations. The main purpose of this study is to examine the impact of double-diffusive convection on magnetic field generation by means of 3D global geodynamo models, in the so-called "top-heavy" regime of double-diffusive convection, when both thermal and compositional background gradients are destabilizing. Using a linear eigensolver, we begin by confirming that, compared to the standard single-diffusive configuration, the onset of convection is facilitated by the addition of a second buoyancy source. We n…
In this work 2D Ising systems were used to simulate the reversals of the Earth's magnetic field. Each spin was supposed to be a ring current in the Earth dynamo and the magnetization to be proportional to the field intensity. Given the relative success of some physical few-discs modeling of this system all the simulations were implemented in small systems. The temperature T was used as a tunning parameter. It plays the role of external perturbations. Power laws were obtained for the distribution of times between reversals. When the system size was increased the exponent of the power law asympt…
We investigate the transition from steady dipolar to reversing multipolar dynamos. The Earth has been argued to lie close to this transition, which could offer a scenario for geomagnetic reversals. We show that the transition between dipolar and multipolar dynamos is characterized by a three terms balance (as opposed to the usually assumed two terms balance), which involves the non-gradient parts of inertial, viscous and Coriolis forces. We introduce from this equilibrium the sole parameter ${\rm Ro}\,{\rm E}^{-1/3} \equiv {\rm Re}\,{\rm E}^{2/3}$, which accurately describes the transition for…
The record of reversals of the geomagnetic field has played an integral role in the development of plate tectonic theory. Statistical analyses of the reversal record are aimed at detailing patterns and linking those patterns to core-mantle processes. The geomagnetic polarity timescale is a dynamic record and new paleomagnetic and geochronologic data provide additional detail. In this paper, we examine the periodicity revealed in the reversal record back to 375 million years ago (Ma) using Fourier analysis. Four significant peaks were found in the reversal power spectra within the 16-40-million…
Field reversals are the most spectacular changes in the geomagnetic field but remain little understood. Paleomagnetic data primarily constrain the reversal rate and provide few additional clues. Reversals and excursions are characterized by a low in dipole moment that can last for some 10kyr. Some paleomagnetic records also suggest that the field decreases much slower before an reversals than it recovers afterwards and that the recovery phase may show an overshoot in field intensity. Here we study the dipole moment variations in several extremely long dynamo simulation to statistically explore…
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing dipole-dominated dynamos and the reversing non-dipole-dominated multipolar solutions. We show that, by considering weak initial fields, the above transition disappears and is replaced by a region of bistability. Such a result was also observed in models with free-slip boundaries in which the geostrophic zonal flow can develop and participate to the dynamo mechanism for non…
Choosing a simple class of flows, with characteristics that may be present in the Earth's core, we study the ability to generate a magnetic field when the flow is permitted to oscillate periodically in time. The flow characteristics are parameterised by D, representing a differential rotation, M, a meridional circulation, and C, a component characterising convective rolls. Dynamo action is sensitive to these flow parameters and fails spectacularly for much of the parameter space where magnetic flux is concentrated into small regions. Oscillations of the flow are introduced by varying the flow …
Using a homotopic family of boundary eigenvalue problems for the mean-field $α^2$-dynamo with helical turbulence parameter $α(r)=α_0+γΔα(r)$ and homotopy parameter $β\in [0,1]$, we show that the underlying network of diabolical points for Dirichlet (idealized, $β=0$) boundary conditions substantially determines the choreography of eigenvalues and thus the character of the dynamo instability for Robin (physically realistic, $β=1$) boundary conditions. In the $(α_0,β,γ)-$space the Arnold tongues of oscillatory solutions at $β=1$ end up at the diabolical points for $β=0$. In the vicinity of the d…
The existence of a stably stratified layer underneath the core-mantle boundary (CMB) has been recently revived by corroborating evidences coming from seismic studies, mineral physics and thermal evolution models. Such a layer could find its physical origination either in compositional stratification due to the accumulation of light elements at the top or the core or in thermal stratification due to the heat flux becoming locally sub-adiabatic. The exact properties of this stably-stratified layer, namely its size $\mathcal{H}_S$ and the degree of its stratification characterised by the Brunt-Vä…
Natural dynamos such as planets and stars generate global scale magnetic field despite the inferred presence of small scale turbulence. Such systems are known as large scale dynamos and are typically driven by convection and influenced by rotation. Previous numerical studies of rotating dynamos generally find that the large scale magnetic field becomes weaker as the flow becomes more turbulent. The underlying physical processes necessary for sustaining so-called large scale dynamos is therefore still debated. Here we use a suite of numerical simulations to show that strong large scale magnetic…
The timeline of the Earth's history reveals quasi-periodicity of the geological record over the last 542 Myr, on timescales close, in the order of magnitude, to 1 Myr. What is the origin of this quasi-periodicity? What is the nature of the global events that define the boundaries of the geological time scale? I propose that a single mechanism is responsible for all three types of such events: mass extinctions, geomagnetic polarity reversals, and sea-level fluctuations. The mechanism is fast, and involves a significant energy release. The mechanism is unlikely to have astronomical causes, both …
The migration of U and Th inside a planet is controlled by its oxidation state imposed by the volatile composition. In the deep interior of a planet, an absence of oxidative volatiles will cause U and Th to stay in a state of metal or low valance compounds with a big density. Consequently, they migrate to the bottom of its mantle first, and then are gradually sequestered to its liquid metal core. Earth is rich in oxidative volatiles including water, therefore, U and Th in the core can be moved up by an internal circulation system consisting of the outer core, hot super plumes, asthenosphere an…
This chapter is build from three 1.5 hours lectures given in Udine in april 2018 on various aspects of Earth's core dynamics. The chapter starts with a short historical note on the discovery of Earth's magnetic field and core (section 1). We then turn to an introduction of magnetohydrodynamics (section 2), introducing and discussing the induction equation and the form and effects of the Lorentz force. Section 3 is devoted to the description of Earth's magnetic field, introducing its spherical harmonics description and showing how it can be used to demonstrate the internal origin of the geomagn…
Earth sustains its magnetic field by a dynamo process driven by convection in the liquid outer core. Geodynamo simulations have been successful in reproducing many observed properties of the geomagnetic field. However, while theoretical considerations suggest that flow in the core is governed by a balance between Lorentz force, rotational force and buoyancy (called MAC balance for Magnetic, Archimedean, Coriolis) with only minute roles for viscous and inertial forces, dynamo simulations must employ viscosity values that are many orders of magnitude larger than in the core due to computational …
An Earth-like planetary magnetic field has been widely invoked as a requirement for habitability as it purportedly mitigates the fluxes of ionizing radiation reaching the surface and the escape of neutrals and ions from the atmosphere. Recent paleomagnetic evidence indicates that the nucleation of Earth's inner core, followed perhaps by an increase in geomagnetic field strength, might have occurred close to the Ediacaran period. Motivated by this putative discovery, we explore the ensuing ramifications from the growth or reversals of Earth's dynamo. By reviewing and synthesizing emerging quant…
Torsional Alfv{é}n waves propagating in the Earth's core have been inferred by inversion techniques applied to geomagnetic models. They appear to propagate across the core but vanish at the equator, exchanging angular momentum between core and mantle. Assuming axial symmetry, we find that an electrically conducting layer at the bottom of the mantle can lead to total absorption of torsional waves that reach the equator. We show that the reflection coefficient depends on G Br , where Br is the strength of the radial magnetic field at the equator, and G the conductance of the lower mantle there. …
The Earth acts as a gigantic heat engine driven by decay of radiogenic isotopes and slow cooling, which gives rise to plate tectonics, volcanoes, and mountain building. Another key product is the geomagnetic field, generated in the liquid iron core by a dynamo running on heat released by cooling and freezing to grow the solid inner core, and on chemical convection due to light elements expelled from the liquid on freezing. The power supplied to the geodynamo, measured by the heat-flux across the core-mantle boundary (CMB), places constraints on Earth's evolution. Estimates of CMB heat-flux dep…
We present an attempt to reach realistic turbulent regime in direct numerical simulations of the geodynamo. We rely on a sequence of three convection-driven simulations in a rapidly rotating spherical shell. The most extreme case reaches towards the Earth's core regime by lowering viscosity (magnetic Prandtl number Pm=0.1) while maintaining vigorous convection (magnetic Reynolds number Rm>500) and rapid rotation (Ekman number E=1e-7), at the limit of what is feasible on today's supercomputers. A detailed and comprehensive analysis highlights several key features matching geomagnetic observatio…
Power spectral analyses of the dipole moment of the earth's magnetic field inferred from ocean sediment cores and archeomagnetic data from time scales of 100 yr to 4 Myr have been carried out. The power spectrum is proportional to 1/f where f is the frequency. These analyses compliment previous work which has established a 1/f^2 spectrum for variations at time scales less than 100 yr. Power spectral analyses of inclination and declination inferred from lake sediments from time scales of 10 yr to 30 kyr have also been performed. The spectra are constant above time scales of 3 kyr, proportional …
